The fraction, 22/7, is a close approximation to the value of pi, as Archimedes discovered by circumscribingpolygons around a circle, noting their perimeterP, and taking a ratio to the diameter D of the circle to get π ≈ P/D. Archimedes obtained his estimate of 22/7 (3.142857...) for pi using a circumscribed 96-sided polygon. Ptolemy improved Archimedes' estimate with a 360-sided polygon, obtaining 3,141666..., a value that's correct to three decimal places.

Somewhere in my reading of the history of mathematics, I remember that millet seeds were employed as a method for estimating the value of pi. Alas, a previous article of mine is the only source for this that Google finds. The method is easy, as the figure shows. You toss a handful of millet seed onto a drawing a circle inscribed in a square, then you count how many seeds have landed on the circle, and how many there are in total. The ratio of these numbers is an estimate of the ratio of the area of the circle to the area of square, from which pi may be calculated.

A square and an inscribed circle populated with random points to estimate pi.

Various physical factors such as the aim of the gun, wind speed and direction, etc., will diminish the randomness of the shot distribution. To counter this, Dumoulin and Thouin used a random selection of the points (20,000) to normalize the distribution, and they used the rest (10,000) to estimate pi.[1-2]